From faults to earthquakes: scaling relations · From faults to earthquakes: brittle strain The...
Transcript of From faults to earthquakes: scaling relations · From faults to earthquakes: brittle strain The...
From faults to earthquakes: scalingrelations
Displacement versus length of faults
What emerges from this data is a linear scaling
between displacement, U , and fault length, L:
U = ηL
Coseismic slip versus rupture length
What emerges from this data is that co-seismic
stress drop is constant over wide range of
earthquake sizes
Recall that the stress drop, ∆τ is given by:
∆τ ∝ γ∆U
r
Thus, the constancy of ∆τ implies linear
scaling between co-seismic slip, ∆U , and
rupture dimension, r:
∆U = ηr
From faults to earthquakes: brittlestrain
The geometric moment for faults is:
Mf = UAf ,
where U is the mean geological displacement
on a fault of area Af .
Similarly, the geometric moment for
earthquakes is:
Me = ∆UAe,
where ∆U is the mean co-seismic slip on a
rupture of area Ae. Thus, Me is the seismic
moment divided by the shear modulus.
Brittle strain can be expressed in two ways
[Kostrov, 1974]]:
From faults:
εij =1
2V
∑
k
[Mf ij]k
From earthquakes:
εij =1
2V
∑
k
[Meij]k
To illustrate the logic behind those equations,
consider the simple case of a plate of brittle
thickness W ∗ and length and width l1, l2 being
extended in the x1 direction by a population of
parallel normal faults of dip ϕ.
The mean displacement of the right-hand face
is:
U =∑
k
Uk cos ϕL2
k sin ϕ
W ∗l2
which may be re-arrange to give:
U
l1= ε11 =
cos ϕ sin ϕ
V
∑
k
UkL2
k
Geodetic data may also be used to compute
brittle strain.
εgeologic
Advantages:
long temporal sampling (Ka, Ma)
Disadvantages:
only fault that are exposed at the surface
cannot discriminate seismic from aseismic
εgeodetic
Advantages:
counts all contributing sources, buried or not
Disadvantages:
Short temporal window
εseismic
Advantages:
Spatial resolution better than that of the
geologic
Disadvantages:
Very short temporal window
Owing to their contrasting perspective, it is
useful to compare:
εgeologic versus εseismic
εgeodetic versus εseismic
εgeologic versus εgeodetic
Steven Ward has done exactly this for the
United States:
What does it mean?
For southern and northern California,
Mgeodetic/Mgeologic ≈ 1.2.
For California: Mseismic/Mgeologic ≈ 0.9.
For California:
Mseismic/Mgeodetic ≈ 0.86 − 0.73.
Recommended reading:
Scholz C. H., Earthquake and fault populations
and the calculation of brittle strain,
Geowissenshaften, 15, 1997.
Ward S. N., On the consistency of earthquake
moment rates, geological fault data, and space
geodetic strain: the United States, Geophys. J.
Int., 134, 172-186, 1998.
Paleoseismology
What can we learn from precariousrocks?
In the 1989 oblique-slip Loma Prieta
earthquake in California, there were
numerous reports of massive objects (e.g.,
cars) that were thrown into the air,
indicating that at least locally the ground
accelerations exceeded 1 g.
Precarious boulders may be used to place
limits on the amount of shaking in the past.
Field tests and modeling of the forces required
to topple the boulders indicate that
accelerations of greater than 0.2 g would
knock over the more precarious boulders,
whereas accelerations of 0.3-0.4 g would be
required for the ”semi-precarious” boulders.
Such numbers provide very useful
paleoseismological limits on the magnitude
of past shaking.
What can we learn from coral heads?
Trench
Fissure filling
Recurrence intervals
Stratigraphic and structural relationships
Offset of a channel
Coke can